FAULHABER POLYNOMIALS AND RECIPROCAL BERNOULLI POLYNOMIALS
FAULHABER POLYNOMIALS AND RECIPROCAL BERNOULLI POLYNOMIALS
About four centuries ago, Johann Faulhaber developed formulas for the power sum 1n+2n+⋯+mn in terms of m(m+1)∕2. The resulting polynomials are called the Faulhaber polynomials. We first give a short survey of Faulhaber’s work and discuss the results of Jacobi (1834) and the less known ones of Schröder (1867), which …